Fermions scattering in a three-dimensional extreme black-hole background

The absorption cross section for scattering of fermions off an extreme BTZ black hole is calculated. It is shown that, as in the case of scalar particles, an extreme BTZ black hole exhibits a vanishing absorption cross section, which is consistent with the vanishing entropy of such an object. Additionally, we give a general argument to prove that the particle flux near the horizon is zero. Finally, we show that the reciprocal space introduced previously in [1] gives rise to the same result and, therefore, it could be considered as the space where the scattering process takes place in an AdS spacetime.